Outlier in statistics, data science & data analysis

What is outlier?

An outlier is an extremely high/big or low/small value compared to other values.

For example: You have numbers like 11, 15, 22, 34, 20,31, 29, 100, -150. Here you can see that 11, 15, 20, 22, 29, 31 and 34 are quite near.If you compare the distance or difference of these values with each other then you will see that there is not that much difference. So these values are not outliers. There is another value of 100 and -150. Now if you compare 100 with other values then you will see 100 is very big/high from other values and -150 is very small/low than other values means 100 and -150 are so far from other values. So you can say that 100 and -150 both are outliers.

Removing Outliers using IQR

IQR stands for inter quartile range. You have already learned about quartiles. Let's use that to find outliers.
But take one thing in mind:
A data value less than Q₁-1.5(IQR) or greater than Q₃+1.5(IQR) can be considered as outlier.

Steps of removing outliers using IQR
Step 1:
Arrange the data in order from lowest to highest and find Q₁ and Q₂

Step 2:
Find the interquartile range= Q₃-Q₁

Step 3:
Multiply IQR by 1.5

Step 4:
Subtract step 3 from Q₁ and Q₃

Step 5:
Check the data set for any data value that is smaller than Q₁-1.5(IQR) or larger than Q₃+1.5(IQR)


Example
Find the outliers from the following data set.
11,13,27,35,29,5,70,33

Arrange the data in ascending order:
5,11,13,27,29,33,35,70

Get Q₁ and Q₃
Q₁=(11+13)/2=12
Q₃=(33+35)/2=34

Interquartile range=Q₃-Q₁=34-12=22

Multiply IQR by 1.5
22*1.5=33 Subtract IQR from Q₁ and Q₃
12-33=-21
34+33=67

Check in the dataset that if there is any value smaller than -21 and a greater value than 67. The smaller values will consider as an outlier and the greater value will consider as the outlier.
There is no smaller value than -21 but have a greater value than 67 and that is 70. So 70 is an outlier.